With the increasing trend in construction of tunnels in the last decade, especially in the mountainous areas and under unsymmetrical stress states in the slopes, the analysis of these tunnels needs particular attention. The rock slopes located in the mountainous areas have usually a complicated topography. Among these slopes, convex slopes which have curvature in the plan can be mentioned. The analysis of the interaction of the tunnels excavated in these types of slopes need to be performed in three dimension. In the interaction analysis of tunnel excavation in slopes which is under unsymmetrical stress state, analytical methods such as convergence-confinement method cannot be involved to solve the problem. Furthermore, use of 2D analyses for excavation of tunnels in the convex slope which has 3D nature, can lead to erroneous results. Also, in jointed rocks, the failure is often associated with slip along the joints; therefore, use of discontinuum modeling is more appropriate. In this article, the excavation of tunnels in the convex rock slopes is dealt with using discrete element method. The aim of this study is the investigation on the stability of tunnels excavated in convex slopes and comparison of 2D and 3D distinct element analyses in this respect.


Stability analysis of underground engineering works has been a challenging and difficult subject in geomechanics. From the early rock load concepts proposed by Terzaghi (1946) to the three dimensional numerical analysis methods now available, there has always been an effort by engineers and researchers to investigate the behavior of excavations in various grounds from soft soils to hard rocks under different stress conditions. Tunnels are attractive alternatives in the mountainous areas to pass through a convex slope, so investigation on excavation of tunnel in these slopes particularly in the jointed rock mass is an important problem.

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